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R.K. Ahrenkiel, W. Metzger, M. Page, and 

R. Reedy

National Renewable Energy Laboratory 

J. Luther and J. Dashdorj

Colorado School of Mines 

Prepared for the 31st IEEE Photovoltaics Specialists 

Conference and Exhibition 

Lake Buena Vista, Florida 

January 3–7, 2005 

February 2005 • NREL/CP-520-37438 

Relationship of Recombination 

Lifetime and Dark Current in 

Silicon p-n Junctions 
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Relationship of Recombination Lifetime to Dark Current 

In Silicon p-n Junctions 

Richard K Ahrenkiel , Wyatt K Metzger, Matthew Page, and Robert Reedy, National Renewable 

Energy Laboratory, Golden, Colorado, and Joseph Luther and Jamiyana Dashdorj, Department of 

Physics, Colorado School of Mines, Golden, Colorado 

ABSTRACT

Measurement of recombination and minoritycarrier lifetimes has become a central activity in

photovoltaic technology. The primary 

measurement techniques for silicon technologies

are based on photoconductive decay (PCD) and

microwave reflectance (mPCD). The

measurement of the correct recombination 

lifetime depends on the carriers being confined to 

a given spatial region of a diagnostic structure. 

The electric field of the PN junction separates the 

charges, and the measured decay time does not

represent the real minority-carrier lifetime. In

these cases, the measured quantity is a function

of the true lifetime and the sample structure. 

Here, we examine these effects, both

experimentally and theoretically, for the n+

-p 

device structure common to terrestrial 

photovoltaics. 

INTRODUCTION 

In this work, we measured the recombination 

lifetime of some single crystal, p-type silicon

wafers under a number of conditions. The 

lifetimes were measured by resonant coupled

photoconductive decay (RCPCD). We first 

measured the lifetime of the wafers as received

from the vendor, and then in a passivating

solution of iodine methanol. The latter process

usually produced a large lifetime increase as the 

surface recombination becomes negligible. Next, 

an n+

-p junction was formed by phosphorous

diffusion, and the lifetime was re-measured. The

measured lifetime of the n

+

-p device always

became larger than the bulk lifetime. From the 

asymptotic decay time, the dark current, J0, could

be computed with recently developed theory 

[1,2,3]. 

Secondary ion mass spectroscopy (SIMS)

was used to measure the phosphorous profile 

after the P-diffusion. The peak P-concentration

was about 1 x 1019

 cm

-3

 and the diffusion depth

is 0.12 μm. 

Open-circuit voltage decay has been

analyzed by many authors [4,5,6,7]. Both device

simulation theory and a simple analytical model 

of carrier recombination in a p-n junction device

produced an increased carrier lifetime in the

device. The latter model suggests that the 

measured lifetime in a p-n device is a function of

J0. In other words, by measuring the

photoconductive lifetime of the device, one can

directly evaluate the dark current value of that 

device. The n

+

-layer was then removed by

etching, and the bulk lifetime was re-measured.

This procedure was followed to evaluate the

parallel effects of phosphorous gettering during

production, producing the lifetime increase in the

junction device. The experimental results for a 

number of single crystal wafers will be presented

and compared with theory. 

MEASUREMENT TECHNIQUE 

The PCD measurements were made using

our RCPCD system [8]. The light source is a 

Coherent Infinity XPO optical parametric

oscillator (OPO). The OPO was set up in the

idler mode and is tunable from about 710 nm to 

about 2200 nm. The pulse width is 5 ns FWHM 

and the pulse energy was controlled by the

insertion of calibrated neutral density filters. The

quantity measured by PCD is:

 (1) 

∆σ(t) = q( ) ∆n(t)μ n + ∆p(t)μ p .

Here, ∆n(t) an ∆p(t) are the excess carrier

densities of electrons and holes, respectively.

Also, μn and μp are the minority-carrier mobilities

of electrons and holes. We have shown in a

previous paper that the long-term decay of

excess majority carriers in a p-n device is: 

∆n(t) = ∆n0 exp −qJ0t

KTC

⎛

⎝

⎜ ⎞

⎠

⎟

 (2) 

Here, J0 is the reverse saturation current of the 

p-n device, and C is the junction capacitance.

This expression is applicable when the opencircuit voltage is less than the thermal voltage,

KT, or about 25 mV at 300 K. This time constant 

is commonly much larger than the recombination

lifetime that is a factor in J0. This equation 

assumes an ideality factor of unity. The physical

source of the decay process is the discharge of 

1 
the open-circuit voltage. The junction capacitance

discharges through the forward-biased PN

junction, and the discharge rate is inversely 

proportional to J0. The charge separation process

occurs rapidly after the absorption of a light 

pulse. The first part of the process is the

diffusion transit time to the junction. When a

photon is absorbed at a distance d from the

junction, the diffusion transit time is

approximately:

τ D = d2 / π2D (3) 

Here D is the minority-carrier diffusivity and τD is 

the transit time. For electrons generated in the 

base of the device, those located at a diffusion

length or less, are collected by the junction. For 

a typical CZ silicon p-type wafer with a doping 

level of 1 x 1015

 cm

-3, the computed diffusion

transit time for electrons at one diffusion length is 

9 ns. Thus, this process is very fast compared to

typical silicon recombination times. More 

accurate calculations will be shown in the

modeling section of this manuscript. 

 

EXPERIMENTAL RESULTS 

We will first show RCPCD measurements on

a 10 ohm-cm p-type substrate prior to diffusion.

The substrate was a standard quality, p-type

commercial wafer grown by the CZ technique. 

The data of curve A were obtained for the asreceived wafer. The low-injection lifetime here is

about 11.6 μs. The data of curve B were

obtained from the same wafer after cleaning in

HF and immersion in an iodine/methanol solution.

This process passivates the surface: ie., reduces

[9] the surface recombination to very low values.

The low-injection lifetime increased to about 48 

μs as a result of passivation. 

The data of Fig. 2, curve B was produced by

diffusing n+ regions onto both surfaces of the

wafer of Fig. 1. The p-n junction that was formed

dramatically changed the PCD. We attribute the

large increase in PC lifetime to charge separation

[3]. 

An alternative explanation for the lifetime

increase (curve B) is that defects are removed 

(gettered) by the phosphorous diffusion. To

check this hypothesis, the phosphorous layer 

was removed by etching and the lifetime was remeasured in air as shown in Figure 3, Curve B. 

Curve A is the data from the virgin sample. We

conclude, therefore, that impurity gettering is not 

a factor in the lifetime increase shown in Fig. 2, 

curve B, as the lifetime actually decreases after

the n+

 removal.

Fig. 1. Curve A is the PCD decay of a p-type CZ

wafer in air environment. Curve B is the PCD

decay with the wafer immersed in iodine/ 

methanol solution. Prior to the latter process, the

wafer was etched in HF. 

Fig. 2. The PCD decay of the wafer of Fig. 1 in

iodine methanol solution (A). Curve B is the PCD

measurement (in air) after n+

 diffusion. 

 

Fig. 3. The PCD decay in air ambient of the

same CZ wafer after etching of the n+ layer (B). 

The decay of the virgin wafer is shown in curve

(A). 

2 
In summary, the charge separation effect 

described these results. The phosphorous 

diffusion and removal produced no net lifetime

increase. 

DEVICE SIMULATION 

Fig. 4 shows the predicted response of the 

device of Fig. 2 using a commercial device

simulation package. In each simulation, a 5 ns 

Gaussian laser pulse containing 2.7x1010

photons/cm2

 injects carriers into either a wafer or 

an n-p-n device structure that is 260 μm thick. 

The simulated parameters include a base, p-type

concentration of 2x1014 holes/cm3

, and SRH

electron and hole lifetimes of 50 μs in the base. 

The n-regions have 1x1019 electrons/cm3

, are 

0.35 μm thick, and are added to the front and

back surfaces of the p-type base. Auger

recombination is dominant in the n-region and

calculated throughout the device with an Auger

coefficient of 6.7x10-32

 cm6/s. Mobility, as a

function of impurity concentration, is calculated

using standard values for silicon, and the model 

by Masetti et al [10]. The drift, diffusion, and 

recombination of excess carriers both during and

after the laser pulse are tracked by

simultaneously solving the hole and electron

continuity equations and Poisson’s equation 

using finite differences [10]. The

photoconductivity signal,σ ph , is calculated from

the equation: 

σph( )t = q d3r

V

∫ μ n(r,t)∆n(r,t)+ μ p [ (r,t)∆p(r,t)]. 

 (4).

Curve A shows the calculated PC decay of a

wafer with a passivated surface and a ShockleyRead-Hall lifetime of 50 μs at low injection. The

plots are presented in arbitrary units of the 

excess conductivity. Curve B shows the 

calculated PC decay after the inclusion of an n+

emitter into the model on both surfaces of the 

wafer.

Fig. 4. The simulated decay curve of a bare,

passivated wafer (curve A), and a wafer with n+

regions on front and back surfaces (curve B). 

The asymptotic lifetime of curve A is just the lowinjection SRH value of 50 μs. For curve B, the 

excess hole concentration in the base becomes

“flat” after about 10 μs, with a density of 8.6 x 

1011 cm-3. From the slope of the low-injection

decay of the pn device, we calculate a decay 

time of about 7 ms. This calculated decay time is

appreciably larger than the measured values of 

Fig. 2. The simulated structure is an “ideal” 

device in the sense that all leakage currents

originate from recombination. The calculated

lifetime is expected to be larger than the 

experimental result. Other leakage sources add

to the J0 of a real device, including surface

currents and shunt paths through the junction. 

The data of Fig. 5 show the PCD decay of a

wafer from another lot, doped p-type with a bulk

carrier concentration varying between 2 X 1015 to 

1 x 10

16

 cm

-3. Four other wafers from this lot

were similarly treated and the experimental

results were nearly identical to those of Fig. 5. 

The data of curve A comes from an as-received

wafer measured in air ambient. The wafer 

underwent a standard phosphorous diffusion,

followed by a HF etch and immersion in iodine

methanol solution. The resulting PCD data is

shown by curve B. The initial decay time is about 

12 μs followed by a much longer photoconductive 

“tail” as the lowest injection levels. The wafer 

was then removed from the solution, rinsed in DI

water and dried. The PCD measurement

produced the data of curve C with an initial decay 

time of about 17 μs. Thus, a slight increase in

decay in air ambient indicates that the surface 

recombination effects are very small in these

structures. These data suggest that the charge

separation effects dominate the surface 

recombination in these PN structures. If one can

generalize these results, then minimal

improvements are made by front surface

passivation in N+

P structures.

Fig. 5. The PCD decay of an as-received wafer

(A) from another lot. Curve B shows the PCD

decay of the wafer after n

+

 diffusion on front and 

back surfaces, and in an iodine methanol

solution. Curve C shows the same wafer

removed to air ambient. 

3 
PROPERTIES OF a n+

-p DEVICE 

Using companion wafers from the same lot as

that of Fig. 5, a small area solar cell was made

from one-fourth of the two-inch wafer. The 

device had fairly poor characteristics, and the

measured J0 was 6.8 μA/cm2

. The junction

capacitance was measured, and J0 was

calculated from Eq. 2 to be 31 μA/cm2. At AM1.5 

irradiance, the Voc was 0.45 volts and Jsc was

24.7 mA/cm2 with a total efficiency of 6.7%. 

Finally, p-n mesa diodes were made by

depositing metal contacts on the n+ layer through

a “shadow mask” on companion wafers. The n+

layer was then etched in unmasked areas, 

completing the fabrication of mesa diodes of

three different sizes; varying from 250 μm to 1.0 

mm. Dark I-V studies showed an increase in the

dark current as the mesa diameter decreased. 

These behaviors are indicative of surface 

leakage a the mesa edge, with the latter 

dominating the bulk recombination processes. 

The open-circuit voltage decay was measured

by using a highly-attenuated, pulsed YAG laser

source for excitation. The YAG wavelength was

1064 nm, and the contacts to the mesa diode 

were connected to a fast, digitizing oscilloscope,

using a 1 meg-ohm input. These data are shown

in Fig. 6 and show a long-term decay time of 2.3 

μs. We compare this value to values of 12 to 17

μs PCD decay time from Fig. 5. The shorter

decay time here is accounted for by the surface 

leakage of the mesa diode. In summary, we

suggest that the RCPCD decay time for a

junction device may be equivalent to the open

circuit voltage decay of a contacted device.

Further work on larger area devices will test this

hypothesis. 

Fig. 6. The measured open-circuit voltage decay

of small area mesa diodes fabricated on a

companion wafer similar to that of Fig. 5. 

CONCLUSIONS 

In this work, we have shown that a n+

junction on a p-type silicon wafer dramatically

changes the photoconductive lifetime. The 

charge separation process produces a decay 

time that is representative of open-circuit voltage

decay, and that it is not the recombination 

lifetime. However, such measurements is an

indicator of the reverse saturation or dark current 

of the device. 

ACKNOWLEDGEMENT 

This work was supported by U.S. DOE

Contract # DE-AC36-99-GO10337. 

REFERENCES 

1. R.K. Ahrenkiel, D. Friedman, W. K. Metzger, 

M. Page, and J. Dashdorj Mat. Res. Soc. Symp. 

Proc. Vol. 799, Z4.6.1 (2004).

2. Jamiyana Dashdorj

, Richard Ahrenkiel, and 

Wyatt Metzger, Mat. Res. Soc. Symp. Proc. Vol. 

799, Z4.5.1 (2004). 

3. W. K. Metzger, R. K. Ahrenkiel, J. Dashdorj, 

and D. Friedman, Phys. Rev. B71, p. 035301, 

(2005).

4. F. A. Lindholm and C. T . Sah, J. Appl. Phys. 

47, 4203 (1976). 

5. S. R. Dhariwal, L. S. Kothari, and S. C. Jain, 

Solid-State Electronics 20, 297 (1977). 

6. J. E. Mahan T. W. Ekstedt, R. I. Fran, and R. 

Kaplow, IEEE Transactions on Electron Devices, 

ED-26, 733 (1979). 

7. R. Gopal. R. Dwivendi, and S. K. Srinvastava, 

J. Appl. Phys. 58, 3476 (1985). 

8. R. K. Ahrenkiel and S. W. Johnston, Materials 

Science and Engineering B102, 161-172 (2003); 

9. H. M’Saad, G. J. Norga, J. Michel, and L. C. 

Kimmerling, AIP Conference Proceedings V306, 

AIP Press, New York, 1994, p 471. 

10. G. Masetti, M. Severi, and S. Solmi, IEEE 

Trans. On Electron Devices, ED-30, 764-769,

(1983). 

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14. ABSTRACT (Maximum 200 Words)

Measurement of recombination and minority-carrier lifetimes has become a central activity in photovoltaic technology. 

The primary measurement techniques for silicon technologies are based on photoconductive decay (PCD) and 

microwave reflectance (mPCD). The measurement of the correct recombination lifetime depends on the carriers 

being confined to a given spatial region of a diagnostic structure. The internal electric fields separate the charges, 

and the measured value does not represent the real minority-carrier lifetime. In these cases, the measured quantity 

is a function of the true lifetime and the sample structure. Here, we examine these effects, both experimentally and 

theoretically, for the n+-p device structure common to terrestrial photovoltaics. 

15. SUBJECT TERMS

PV; measurement of recombination; minority-carrier lifetimes; photoconductive decay (PCD); microwave reflectance 

(mPCD); silicon p-n junctions 

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